// S3C Manifold FPGA Implementation
// Derived from Lean: Semantics/S3C.lean
// Target: Gowin GW1NR-9 (Tang Nano 9K)
// Q16.16 fixed-point arithmetic
// Implements genus-3 topological manifold for audio processing

`timescale 1ns / 1ps

// ═══════════════════════════════════════════════════════════════════════════
// S3C Shell Decomposition: n = k^2 + a
// Computes shell coordinates for integer decomposition
// ═══════════════════════════════════════════════════════════════════════════
module s3c_shell_decomposition (
    input  wire [15:0] n,          // Input sample (unsigned 16-bit)
    output reg  [15:0] k,          // Shell index (coarse handle)
    output reg  [15:0] a,          // Lower offset (medium handle)
    output reg  [15:0] b,          // Upper offset (fine handle)
    output reg  [31:0] mass,       // Intersection form a*b
    output reg  [15:0] width       // Shell width = 2k+1 = a+b+1
);
    // Compute k = floor(sqrt(n))
    // OPTIMIZATION: Use lookup table for sqrt (smaller than hardware sqrt)
    // For 16-bit input, we can use a 256-entry lookup table for sqrt of 0-65535
    
    // Simplified sqrt approximation using binary search
    reg [15:0] sqrt_result;
    reg [15:0] sqrt_low;
    reg [15:0] sqrt_high;
    reg [15:0] sqrt_mid;
    reg [15:0] sqrt_sq;
    
    integer i;
    
    always @(*) begin
        sqrt_low = 0;
        sqrt_high = 16'd256;  // sqrt(65536) = 256
        sqrt_result = 0;
        
        // Binary search for sqrt
        for (i = 0; i < 8; i = i + 1) begin
            sqrt_mid = (sqrt_low + sqrt_high) >> 1;
            sqrt_sq = sqrt_mid * sqrt_mid;
            if (sqrt_sq < n) begin
                sqrt_low = sqrt_mid + 1;
            end else begin
                sqrt_high = sqrt_mid;
            end
        end
        sqrt_result = sqrt_low - 1;
        if (sqrt_result > 255) sqrt_result = 255;
    end
    
    // Compute k, a, b, mass, width
    reg [31:0] k_sq;
    reg [31:0] k1_sq;
    
    always @(*) begin
        k = sqrt_result;
        k_sq = k * k;
        a = n - k_sq[15:0];
        k1_sq = (k + 1) * (k + 1);
        b = k1_sq[15:0] - n;
        mass = a * b;
        width = a + b + 1;
    end
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// S3C 3-Handle Manifold
// Maps audio sample to 3-handle manifold structure
// ═══════════════════════════════════════════════════════════════════════════
module s3c_manifold_handle (
    input  wire [15:0] sample,
    output wire [15:0] handleK,     // Coarse handle (amplitude envelope)
    output wire [15:0] handleA,     // Medium handle (spectral content)
    output wire [15:0] handleB      // Fine handle (phase information)
);
    wire [15:0] k, a, b;
    wire [31:0] mass;
    wire [15:0] width;
    
    s3c_shell_decomposition shell_inst (
        .n(sample),
        .k(k),
        .a(a),
        .b(b),
        .mass(mass),
        .width(width)
    );
    
    assign handleK = k;
    assign handleA = a;
    assign handleB = b;
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// S3C 3-Point Contact Detection
// Detects 3-point contact from manifold handles
// ═══════════════════════════════════════════════════════════════════════════
module s3c_three_point_contact (
    input  wire [15:0] handleK,
    input  wire [15:0] handleA,
    input  wire [15:0] handleB,
    output wire        kappaA,      // Forward spectral prediction
    output wire        kappaB,      // Temporal midpoint
    output wire        kappaC       // Backward phase correction
);
    assign kappaA = (handleA > 0);
    assign kappaB = (handleK > 0);
    assign kappaC = (handleB > 0);
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// S3C J-Score Calculation
// J(n) = ab*F_m + (a-b)*F_p + <chi, F_c>
// ═══════════════════════════════════════════════════════════════════════════
module s3c_j_score (
    input  wire [15:0] handleK,
    input  wire [15:0] handleA,
    input  wire [15:0] handleB,
    output wire [31:0] massResonance,   // ab*F_m
    output wire [31:0] mirrorResonance, // (a-b)*F_p
    output wire [31:0] spectralCoupling, // <chi, F_c>
    output wire [31:0] total            // J(n)
);
    wire [31:0] ab;
    wire [15:0] a_minus_b;
    wire [31:0] abs_a_minus_b;
    
    assign ab = handleA * handleB;
    assign a_minus_b = (handleA >= handleB) ? (handleA - handleB) : (handleB - handleA);
    assign abs_a_minus_b = {16'b0, a_minus_b};
    
    assign massResonance = ab;
    assign mirrorResonance = abs_a_minus_b;
    assign spectralCoupling = {16'b0, handleK};
    assign total = massResonance + mirrorResonance + spectralCoupling;
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// S3C Emission Gate
// Emit only if kappa_A AND kappa_C AND J > 0
// ═══════════════════════════════════════════════════════════════════════════
module s3c_emission_gate (
    input  wire        kappaA,
    input  wire        kappaC,
    input  wire [31:0] jScore,
    output wire        emit
);
    assign emit = kappaA && kappaC && (jScore > 0);
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// S3C Audio Processing Pipeline
// Complete S3C manifold processing for audio samples
// ═══════════════════════════════════════════════════════════════════════════
module s3c_audio_processor (
    input  wire        clk,
    input  wire        rst_n,
    input  wire [15:0] audio_sample,  // Unsigned 16-bit audio sample
    output reg  [15:0] handleK,
    output reg  [15:0] handleA,
    output reg  [15:0] handleB,
    output reg  [31:0] massResonance,
    output reg  [31:0] mirrorResonance,
    output reg  [31:0] spectralCoupling,
    output reg  [31:0] jScore,
    output reg         emit
);
    // Pipeline Stage 1: Manifold handles
    wire [15:0] handleK_stage1, handleA_stage1, handleB_stage1;
    reg [15:0] handleK_stage1_reg, handleA_stage1_reg, handleB_stage1_reg;
    
    s3c_manifold_handle manifold_inst (
        .sample(audio_sample),
        .handleK(handleK_stage1),
        .handleA(handleA_stage1),
        .handleB(handleB_stage1)
    );
    
    always @(posedge clk or negedge rst_n) begin
        if (!rst_n) begin
            handleK_stage1_reg <= 16'd0;
            handleA_stage1_reg <= 16'd0;
            handleB_stage1_reg <= 16'd0;
        end else begin
            handleK_stage1_reg <= handleK_stage1;
            handleA_stage1_reg <= handleA_stage1;
            handleB_stage1_reg <= handleB_stage1;
        end
    end
    
    // Pipeline Stage 2: Contact detection + J-score
    wire kappaA_stage2, kappaB_stage2, kappaC_stage2;
    wire [31:0] massResonance_stage2, mirrorResonance_stage2, spectralCoupling_stage2, jScore_stage2;
    reg kappaA_stage2_reg, kappaC_stage2_reg;
    reg [31:0] massResonance_stage2_reg, mirrorResonance_stage2_reg, spectralCoupling_stage2_reg, jScore_stage2_reg;
    
    s3c_three_point_contact contact_inst (
        .handleK(handleK_stage1_reg),
        .handleA(handleA_stage1_reg),
        .handleB(handleB_stage1_reg),
        .kappaA(kappaA_stage2),
        .kappaB(kappaB_stage2),
        .kappaC(kappaC_stage2)
    );
    
    s3c_j_score jscore_inst (
        .handleK(handleK_stage1_reg),
        .handleA(handleA_stage1_reg),
        .handleB(handleB_stage1_reg),
        .massResonance(massResonance_stage2),
        .mirrorResonance(mirrorResonance_stage2),
        .spectralCoupling(spectralCoupling_stage2),
        .total(jScore_stage2)
    );
    
    always @(posedge clk or negedge rst_n) begin
        if (!rst_n) begin
            kappaA_stage2_reg <= 1'b0;
            kappaC_stage2_reg <= 1'b0;
            massResonance_stage2_reg <= 32'd0;
            mirrorResonance_stage2_reg <= 32'd0;
            spectralCoupling_stage2_reg <= 32'd0;
            jScore_stage2_reg <= 32'd0;
        end else begin
            kappaA_stage2_reg <= kappaA_stage2;
            kappaC_stage2_reg <= kappaC_stage2;
            massResonance_stage2_reg <= massResonance_stage2;
            mirrorResonance_stage2_reg <= mirrorResonance_stage2;
            spectralCoupling_stage2_reg <= spectralCoupling_stage2;
            jScore_stage2_reg <= jScore_stage2;
        end
    end
    
    // Pipeline Stage 3: Emission gate
    wire emit_stage3;
    
    s3c_emission_gate emission_inst (
        .kappaA(kappaA_stage2_reg),
        .kappaC(kappaC_stage2_reg),
        .jScore(jScore_stage2_reg),
        .emit(emit_stage3)
    );
    
    // Output registers
    always @(posedge clk or negedge rst_n) begin
        if (!rst_n) begin
            handleK <= 16'd0;
            handleA <= 16'd0;
            handleB <= 16'd0;
            massResonance <= 32'd0;
            mirrorResonance <= 32'd0;
            spectralCoupling <= 32'd0;
            jScore <= 32'd0;
            emit <= 1'b0;
        end else begin
            handleK <= handleK_stage1_reg;
            handleA <= handleA_stage1_reg;
            handleB <= handleB_stage1_reg;
            massResonance <= massResonance_stage2_reg;
            mirrorResonance <= mirrorResonance_stage2_reg;
            spectralCoupling <= spectralCoupling_stage2_reg;
            jScore <= jScore_stage2_reg;
            emit <= emit_stage3;
        end
    end
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// S3C Testbench
// ═══════════════════════════════════════════════════════════════════════════
module s3c_audio_processor_tb;
    reg clk;
    reg rst_n;
    reg [15:0] audio_sample;
    
    wire [15:0] handleK;
    wire [15:0] handleA;
    wire [15:0] handleB;
    wire [31:0] massResonance;
    wire [31:0] mirrorResonance;
    wire [31:0] spectralCoupling;
    wire [31:0] jScore;
    wire emit;
    
    // Instantiate DUT
    s3c_audio_processor dut (
        .clk(clk),
        .rst_n(rst_n),
        .audio_sample(audio_sample),
        .handleK(handleK),
        .handleA(handleA),
        .handleB(handleB),
        .massResonance(massResonance),
        .mirrorResonance(mirrorResonance),
        .spectralCoupling(spectralCoupling),
        .jScore(jScore),
        .emit(emit)
    );
    
    // Clock generation
    initial clk = 0;
    always #18.5185 clk = ~clk;  // 27MHz
    
    // Test stimulus
    initial begin
        // Initialize
        rst_n = 0;
        audio_sample = 16'd0;
        
        #100;
        rst_n = 1;
        
        #100;
        
        // Test samples (matching Python test)
        audio_sample = 16'd100;
        #100;
        $display("Sample 100: k=%d, a=%d, b=%d, mass=%d, emit=%b", 
                 handleK, handleA, handleB, massResonance, emit);
        
        audio_sample = 16'd256;
        #100;
        $display("Sample 256: k=%d, a=%d, b=%d, mass=%d, emit=%b", 
                 handleK, handleA, handleB, massResonance, emit);
        
        audio_sample = 16'd1000;
        #100;
        $display("Sample 1000: k=%d, a=%d, b=%d, mass=%d, emit=%b", 
                 handleK, handleA, handleB, massResonance, emit);
        
        audio_sample = 16'd5000;
        #100;
        $display("Sample 5000: k=%d, a=%d, b=%d, mass=%d, emit=%b", 
                 handleK, handleA, handleB, massResonance, emit);
        
        audio_sample = 16'd10000;
        #100;
        $display("Sample 10000: k=%d, a=%d, b=%d, mass=%d, emit=%b", 
                 handleK, handleA, handleB, massResonance, emit);
        
        #100;
        $finish;
    end
endmodule